Proportional-Integral-Derivative (PID) controllers are widely used across many industries. PID controllers are relatively easy to implement and relatively simple to tune. In general, a PID controller takes as its input the error (e) from a control system and acts on the error to generate a control output (u). While PID controllers are widely used and provide satisfactory results in many applications, other controllers may also be desired.
Some prior art patents using wavelets in controls include U.S. Pat. No. 5,610,843, which involves control of a Multi-Input, Multi-Output (“MIMO”) system, and provides a method for implementing a controller in a system having many sensors and actuators. Additionally, the disclosure involves computing two transfer functions P and Q (transfer function from actuator to sensor and transfer function matrix from sensor back to actuator) using wavelet transforms on a multi-scale basis. The controller K is then implemented using Q-parameterization as K=(I+PQ)−1 Q.
U.S. Pat. No. 6,480,750 provides means to perform auto-tracking by adjusting the controller (PID) parameters. A wavelet transformation of the control signal and the output signal is done. The result of the analysis is transformed into a system of differential equations. The formulation of the system of differential equations serves to establish a mathematical function which characterizes the response of a plant. Based on the response from the plant it is possible to document changes in the response characteristics of the controlled system. It is possible in this way for the control system to be adapted to simply prescribe operating states of the controlled system which keeps recurring during operation of the controlled system. U.S. Pat. No. 6,497,099 is similar, but has a specific application to a steam turbine.